Power Spectrum of Depth Values 



The third method of representing variability is by the power 

 spectrum j^''"'^'^^'^^"^" The power spectrum U{h) is given by the 

 Fourier transform of the autocorrelation, R . It is the energy per 

 unit bandwidth and thus designed to emphasize the dominant fre- 

 quencies, since the amplitudes are squared. The smoothed power 

 spectrum values were obtained as follows: 



U{h)=^ 



R{o)+ Yj i?{A) (1 + COS—) cos ^^— ^ 



where h= 0, 1, 2, 3 .... n index number of frequency 



(actual frequencies are given 

 by h /{2At) cycles/min, 

 A t = 1/2 min), and 



A = 0, 1, 2, 3 ... . n is the lag number 



The results of the computed power spectra of all the selected 

 isotherms on each section of the cruise were plotted for compari- 

 son in Appendix C . 



One example of the computed power spectrum is shown in 

 figure 8. The importance of the power spectrum lies in the peaks 

 in the curve that indicate frequencies (or periods) in the original 

 data which may have been obscured by "background noise. " Of 

 significance is the fact that this example of power spectrum has a 

 large number of peaks or peak zones ranging in frequency* of 



*Herethe sampling chain is moving through a quasi- stationary field 

 of internal waves and the frequencies discussed are "frequencies of 

 encounter. " The wave lengths are nominal ones computed from the 

 ship speed of 6 knots assuming that the internal waves are essen- 

 tially stationary, i.e. are moving much slower than 6 knots. One 

 should expect broad peaks or "peak zones" as often as narrow peaks 

 if the internal waves are traveling in all directions; e.g. if inter- 

 nal waves of only a very narrow band of frequencies arrived 

 from all directions, the straight track of the ship would intercept 

 apparent wavelengths corresponding to a broad band of fre- 

 quencies. 



19 



